We discuss the transverse momentum Q T distribution of Drell-Yan pair, produced in collisions of transversely polarized protons. We calculate the transversely polarized DrellYan cross section up to O(α s ) in the dimensional regularization, which gives QCD prediction at large Q T . For small Q T , we include all-orders resummation of large logarithms due to emission of soft gluons up to next-to-leading logarithmic accuracy. At intermediate Q T , the resummation formula is matched with the fixed-order α s perturbative results in a systematic way, and we derive the cross section with uniform accuracy over the entire range of Q T .Hard processes with polarized beams and/or target enable us to study spindependent dynamics of QCD. The helicity distribution ∆q(x) of quarks inside nucleon has been measured in polarized DIS experiments, and also ∆G(x) of gluon has been estimated from the scaling violations of them. On the other hand, the transversity distribution δq(x), i.e. the distribution of transversely polarized quarks inside transversely polarized nucleon, cannot be measured in the inclusive DIS due to its chiral-odd nature, 1) and remains as the last unknown distribution at the leading twist. Transversely polarized Drell-Yan (tDY) process is one of the processes where δq(x) can be measured, and has been undertaken at RHIC-Spin experiment. 2)We develop the QCD prediction of tDY cross section, dσ/dQ 2 dQ 2 T dydφ, differential in the transverse momentum Q T and rapidity y of the produced lepton pair, as well as in the dilepton invariant mass Q and in the azimuthal angle φ of one of the leptons with respect to the incoming nucleon's spin axis. Although this Q T -and y-differential cross section is fundamental in view of comparison with experiment, the corresponding formula has been unknown so far even in the leading order (LO) in QCD: the lepton-pair production with finite Q T via the Drell-Yan mechanism has to be accompanied by the radiation of at least one recoiling parton, so the LO term of the cross section is of O(α s ). The corresponding one-loop calculation of the LO term requires the phase space integration separating out the relevant transverse degrees of freedom, to extract the cos(2φ) dependence which is characteristic of the spin-dependent cross section of tDY. 1) In the dimensional regularization, in particular, the relevant phase space integration in D-dimension is rather cumbersome compared with unpolarized and longitudinally polarized cases. Furthermore, at small Q T ("edge regions of the phase space"), the radiation of soft gluon produces

It has recently been suggested that collisions of transversely polarized protons and antiprotons at the GSI could be used to determine the nucleon's transversity densities from measurements of the double-spin asymmetry for the Drell-Yan process. We analyze the role of higher-order perturbative QCD corrections in this kinematic regime, in terms of the available fixed-order contributions as well as of all-order soft-gluon resummations. We find that the combined perturbative corrections to the individual unpolarized and transversely polarized cross sections are large. We trace these large enhancements to soft gluon emission near partonic threshold, and we suggest that with a physically-motivated cut-off enhancements beyond lowest order are moderated relative to resummed perturbation theory, but still significant. The unpolarized dilepton cross section for the GSI kinematics may therefore provide information on the relation of perturbative and nonperturbative dynamics in hadronic scattering. The spin asymmetry turns out to be rather robust, relatively insensitive to higher orders, resummation, and the cut-offs.

A novel scheme for the focusing of high-energy leptons in future linear colliders was proposed in 2001 [P. Raimondi and A. Seryi, Phys. Rev. Lett. 86, 3779 (2001)]. This scheme has many advantageous properties over previously studied focusing schemes, including being significantly shorter for a given energy and having a significantly better energy bandwidth. Experimental results from the ATF2 accelerator at KEK are presented that validate the operating principle of such a scheme by demonstrating the demagnification of a 1.3 GeV electron beam down to below 65 nm in height using an energy-scaled version of the compact focusing optics designed for the ILC collider.

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